1. Field of the Invention
The present invention relates to a method and an apparatus for detecting the concentration of a desired substance in a solution as well as a diluting preparation apparatus for diluting and preparing a solid and a high concentration agent to a predetermined concentration.
2. Description of the Prior Art
Detection of the concentration of a specific substance in a solution is universally required in almost all industrial fields. Particularly, in industrial fields associated with semiconductors and liquid crystals, the ingredients and concentration of a solution must be frequently more strictly controlled and managed compared with those in other fields.
In fabrication steps for semiconductors for example, an alkali developing solution for use in development of a positive photoresist is a deciding factor to improve the resolution, dimensional accuracy, and stability, etc., of the photoresist, so that it is necessary to strictly control the ingredients and concentration of the solution while adjusting the positive photoresist used.
For a diluted hydrofluoric acid (an aqueous solution of hydrofluoric acid) for use in etching a silicon oxide film, etc., it is needed to accurately control the rate of etching or the amount of etching corresponding to the thickness of the silicon oxide film, etc. In order to achieve such a requirement it is needed to strictly control the concentration of the diluted hydrofluoric acid.
Japanese patents No. 2090366 (JP, 6-7910,B), No. 2751849 (cf. JP, 8-62852,A), No. 2670211(cf. JP, 6-29207,A; corresponding to U.S. Pat. No. 5,843,602) disclose a dilution apparatus for a developing stock solution equipped with control means for such concentration.
Hereupon, although agents for which strict concentration control is required are shipped to makers using such agents after makers supplying such agents dilute and adjust the concentrations of the agents to desired concentrations, recently there are increased cases in which the makers using such agents dilute and adjust high concentration agents to desired concentration ones.
These dilution apparatuses are classified to continuous ones disclosed in Japanese patents No. 2090366(JP, 6-7910, B) and No. 2751849, and to a batch one disclosed in Japanese Patent No. 2670211.
It is known that the electrical conductivity of a solution is varied depending upon the concentration and temperature of the solution. It is further known that in a wide temperature range and in a wide concentration range a relationship between concentration and electrical conductivity at a predetermined temperature and a relationship between electrical conductivity and temperature at a predetermined concentration do not satisfy a linear equation.
For this, in prior art measurements, it is assumed that after there are set temperature upon the measurement and concentration to be desired in the vicinity of the setting temperature and concentration the electrical conductivity is varied in terms of a linear equation of the concentration and it is further assumed that a change rate of the electrical conductivity upon the temperature being varied is unchanged without depending upon the concentration, and in the vicinity of the setting temperature and concentration, the concentration is estimated by measuring the electrical conductivity and the temperature.
Since the temperature of a solution is typically different from the setting temperature, the measurement for the solution is performed under the conditions where the temperature of the solution is kept at the setting temperature by passing the solution through a temperature controller.
In the continuous dilution apparatus, as disclosed in Japanese patents No. 2090366 (JP, 6-7910, B) and No. 2751849, there are set desired concentration and temperature, and the concentration of an agent is measured at all times while continuously supplying the agent or water, and the amount of supply of the agent or water is adjusted for dilution in response to the variations of the concentration.
Since the adjustment is performed in succession, it is desirable that the concentration measurement for agents is performed in real time, but the measurement of the concentration is retarded by the time that the solution passes through a temperature controller, so that excess and deficiency of an agent or water are likely to happen and hence greater concentration variations are likely to occur for a fluid taken out from a stirring tank into a storage tank.
The batch method is a method as disclosed in the Japanese Patent No. 2670211 wherein there is repeated an operation, where after an agent is diluted with water, the concentration of a diluted solution is measured to calculate the necessary amount of the agent and water and add them into a stirring tank until a solution that has a purposed concentration is obtained. Since in the present system, supply of the agent or water is not performed anew until the concentration is estimated, there can be taken at need the time for which the solution passes through the temperature controller, so that the concentration measurement is achieved more accurately than that of the continuous system. However, the batch system suffers from a difficulty that preparing time is prolonged because there is increased the time needed for the solution to pass through the temperature controller.
Further, the prior art measurement with a conductivity meter suffers from another difficulty that numerical values are inaccurate. Provided variations of the numerical values are large, the allowable concentration of an agent to be prepared must be more narrowed corresponding to those variations than that instructed by a user.
Makers using agents who require convenient concentration control desire that the aforementioned difficulties are solved as quickly as possible.
Although for accurately preparing an agent to a desired concentration it is essential to accurately detect the concentration of the agent, there is a relationship expressed by a linear equation in a predetermined temperature range and at a predetermined temperature both defined by the agent between the concentration of the agent and the electrical conductivity of the solution, so that it is conventionally general that for an electrical conductivity meter used for the control of the concentration there is grasped a relationship between the electrical conductivity of the solution at a predetermined temperature and the concentration of an agent and a relationship between the electrical conductivity of the solution at a certain temperature and the temperature, and that the concentration of the agent is calculated upon measuring the electrical conductivity of the solution, based upon a measured value.
More specifically, there is estimated by an experiment a linear equation Dt=axe2x80x2C+bxe2x80x2 (Dt indicates an electrical conductivity, C concentration, and axe2x80x2 and bxe2x80x2 indicate constants.) representative of a relationship between the electrical conductivity of a solution and the concentration of an agent at a certain temperature (setting temperature t). Then, it is assumed that the electrical conductivity becomes higher by d every time the measurement temperature of the electrical conductivity becomes higher by 1 degree than the setting temperature t, and the d is estimated by the experiment. Accordingly, provided the electrical conductivity when the temperature of a solution is T is DT, the electrical conductivity Dt of the solution at the setting temperature t is represented by a formula Dt=Dtxe2x88x92d(Txe2x88x92t). In contrast, since Dt=axe2x80x2C+bxe2x80x2, DTxe2x88x92d(Txe2x88x92t)=axe2x80x2C+bxe2x80x2, and solving the equation with respect to C, C=(DTxe2x88x92d(Txe2x88x92t)xe2x88x92bxe2x80x2)/axe2x80x2. Even when the measurement temperature of the electrical conductivity is shifted from the setting temperature t, temperature compensation is achieved using the foregoing last equation, and hence the concentration is calculated from the electrical conductivity.
However, since the prior art presupposes the assumption that in a predetermined temperature and concentration region determined by the agent the electrical conductivity becomes higher by d every time the measurement temperature of the electrical conductivity becomes higher by 1 degree, accurate concentration of the solution can be calculated provided the temperature of the solution is the same as the setting temperature, but when the temperature of the solution is shifted from a predetermined measurement temperature, there is produced an error between actual concentration and calculated concentration. Thus, the prior art suffers from a difficulty that it is difficult to grasp the concentration with accuracy tolerable against the conditions where strict concentration control management is needed.
The prior art further suffers from a difficulty associated with the foregoing difficulties, as mentioned in the foregoing Japanese patent No. 2090366(JP, 6-7910, B), that the electrical conductivity is needed to be measured in the state where the temperature of a solution is kept at the setting temperature with the aid of a temperature controller. For this, there is required a heat source for a temperature keeping apparatus and the like and installation investment for the temperature controller, resulting in the high cost of dilution preparing of an agent and complicated work. There is further another difficulty that when the concentration measurement is continuously performed with the aid of a temperature controller, there is the need of keeping the temperature at the set one, so that the measurement is retarded by the time required for the solution to pass through the temperature controller also as disclosed in Japanese patents No. 2090366 (JP, 6-7910) and No. 2751849.
It is therefore an object of the present invention to provide a method and an apparatus for detecting the concentration of a solution and an apparatus for diluting and preparing an agent wherein the concentration of a solution can be obtained accurately and reproducibly even without strict temperature control, and the concentration can be obtained in a real time, and further the cost of dilution and preparing of an agent can be reduced and diluting and preparing work can be simplified.
The present inventors have found solving means to complete the present invention as a result of the pursuit of our studies to solve the aforementioned difficulties.
The present invention relates to a method for detecting the concentration of a solution comprising a step for measuring the electrical conductivity and temperature of the solution and a step for calculating the concentration of a desired substance in the solution from the foregoing electrical conductivity and the foregoing temperature based upon the following equation:
C=(Dxe2x88x92aTxe2x88x92b)/(AT+B)xe2x80x83xe2x80x83(1)
wherein C is the concentration of a desired substance, D is the electrical conductivity of a solution at temperature T, T is the temperature of the solution, and A, B, a, and b represent a constant, respectively.
The present invention further relates to the aforementioned method for detecting the concentration of a solution wherein the constants A, B, a, b in the equation are values obtained by measuring the electrical conductivity of the solution at the plurality of the temperatures for each solution containing the same desired substance with the plurality of the concentrations while applying the least squares method to a measured result.
The present invention further relates to the aforementioned method wherein the constants A, B, a, b are values obtained by a method comprising a first step for measuring the electrical conductivity at a plurality of temperatures for each solution containing the same agent with a plurality of the concentrations, a second step for deriving a linear equation by the least squares method for a relationship between the temperature and the electrical conductivity with each concentration, a third step for substituting the plurality of the temperatures for each of the foregoing linear equation and calculating the electrical conductivity at each temperature, a fourth step for deriving a linear equation with the least squares method with respect to a relationship at each temperature in the third step, and a fifth step for deriving linear equations w=AT+B and z=aT+b with temperature for each of the inclination w and the concept of each linear equation obtained in the fourth step.
The present invention further relates to the foregoing method for detecting the concentration of a solution where in the plurality of the temperatures are included within a temperature range of xc2x15 degrees of the desired temperature.
The present invention still further relates to the aforementioned method for detecting the concentration of a solution wherein the plurality of the temperatures are included within a temperature range of xc2x110 degrees of the desired temperature.
The present invention furthermore relates to a method for detecting the concentration of a solution where in the solution is an aqueous solution.
The present invention still furthermore relates to the aforementioned method for detecting the concentration of a solution wherein the solution contains only one kind of a solute.
The present invention further relates to a method for diluting and preparing an agent to a desired concentration utilizing the aforementioned method for detecting the concentration of a solution.
The present invention relates to the aforementioned method for diluting and preparing an agent comprising a first step wherein the agent is mixed with water into an aqueous solution, a second step wherein the concentration of the agent in the aqueous solution is detected, and a third step wherein an agent or water is added to the aqueous solution to adjust the concentration of the agent to a desired concentration.
The present invention further relates to the aforementioned method for diluting and preparing an agent wherein at least the second step and the third step are controlled with a computer program.
The present invention still further relates to a concentration detecting apparatus comprising electric conductivity measuring means and arithmetic operation means for detecting the concentration of a desired substance in a solution by the arithmetic operation means based upon the electric conductivity of the solution measured by the electric conductivity measuring means, the arithmetic operation means calculating the following equation:
C=(Dxe2x88x92aTxe2x88x92b)/(AT+B)xe2x80x83xe2x80x83(1)
wherein C designates the concentration of a desired substance, D is electric conductivity of the solution upon temperature T, T is the temperature of the solution, and A, B. a, and b each denote a constant.
The present invention yet still further relates to the concentration detecting apparatus wherein the constants A, B, a, b in the equation (1) are values by measuring for each of the solutions containing the same desired substance at a plurality of concentrations, the electric conductivities at a plurality of temperatures and by applying the least square method thereto.
The present invention further relates to the concentration detecting apparatus wherein the constants A, B, a, b are values calculated for solutions containing the same agent with a plurality of concentrations by a method comprising: a first step for measuring electric conductivities at a plurality of temperatures, a second step for deriving a linear equation with the method of least square for a relationship between the temperature and the electric conductivities at the respective concentrations, a third step for substituting the aforementioned plurality of temperatures for each of the linear equations to calculate the electric conductivity at each temperature, a fourth step for deriving a linear equation by the least squares method with respect to a relationship between the electric conductivity and the concentration at each temperature in the third step, and a fifth step for deriving linear equations w=AT+B and z=aT+b with respect to temperature for each inclination w and an intercept z of each linear equation obtained in the fourth step.
The present invention relates to the aforementioned concentration detecting apparatus wherein the plurality of temperatures are included within a temperature range of 5xc2x1 degrees.
The present invention further relates to the aforementioned apparatus wherein the plurality of temperatures are included within a desired temperature range of xc2x110 degrees.
The present invention relates to the aforementioned concentration detecting apparatus wherein a solution to be measured is an aqueous solution.
The present invention further relates to the aforementioned concentration detecting apparatus wherein a solution to be measured involves only one kind of solute.
The present inventors have found the following two facts as a result of thorough investigation on why variations of numerical values are large: that (1) air bubbles remaining in a measuring chamber sharply influences measured values, (2) there is left behind a solution used at the previous time of measurement in the measuring chamber depending upon the configuration of the inside of the measuring chamber, which solution is then mixed with a fluid flowing into next time to change the concentration of the solution. More specifically, the configuration of the measuring chamber maybe one having an outlet for aqueous solution at the head of the chamber and is desirable for the configuration which prevents any fluid from remaining in the measuring chamber The configuration is preferable which is continuously reduced in size toward the outlet for aqueous solution for example, but it is not limited thereto.
The present invention accordingly also relates to the aforementioned concentration detecting apparatus wherein electric conductivity measuring means includes a measuring chamber provided with an inlet for aqueous solution and a flow outlet at the head, and a horizontal cross sectional area of the measuring chamber is continuously reduced toward the outlet for aqueous solution.
A measuring rod is disposed in the measuring chamber, which rod has a through-hole therethrough. Provided that air bubbles flow into the through-hole, it influences measured values if it is not removed quickly. To improve such a situation, the present inventors have found that a water flow may be formed in the direction of the through-hole in the measuring chamber.
A further one inlet for aqueous solution is for example preferably provided in the vicinity of an intersection between an extension line of the through-hole and a wall surface of the measuring chamber, but the present invention is not limited thereto.
The present invention accordingly further relates to the aforementioned concentration detection apparatus wherein the measuring chamber includes a measuring rod disposed there in having a through-hole therethrough, and further, another inlet for aqueous solution is provided in the vicinity of an intersection between an extension line of the through-hole and a wall surface of the measuring chamber.
The present invention further relates to the aforementioned agent diluting preparation apparatus equipped with the aforementioned concentration detection apparatus for diluting and preparing an agent to a desired concentration by mixing the agent with water.
The present invention still further relates to the aforementioned agent diluting and preparing apparatus including a diluting and preparing tank, mixing means for mixing an agent with water into an aqueous solution, and concentration adjusting means for adjusting the concentration of the agent to a desired one by adding an agent or water into an aqueous solution based upon detected concentration.
The present invention furthermore relates to the aforementioned agent diluting and preparing apparatus wherein at least the concentration detection apparatus and the concentration adjusting means are controlled with a computer program.
The present invention further relates to the aforementioned agent diluting and preparing apparatus wherein upon measuring the electric conductivity and temperature part of the aqueous solution is temporarily sent from the diluting and preparing tank to the electric conductivity measuring means of the concentration detecting apparatus, and the electric conductivity measuring means includes a measuring chamber having an inlet for aqueous solution and an outlet for aqueous solution at the head thereof, and further a horizontal cross sectional area of the measuring chamber is continuously reduced toward the outlet for aqueous solution.
The present invention further relates to the aforementioned agent diluting and preparing apparatus wherein the measuring chamber includes a measuring rod disposed in the measuring chamber, and the measuring rod has a through-hole, and further the measuring rod further includes another inlet for aqueous solution in the vicinity of an intersection between an extension line of the through-hole and a wall surface of the measuring chamber.
The above and other objects, advantages and features of the present invention will be more apparent from the following description taken in conjunction with the accompanying drawings.